The biggest mystery for me is how the spinning heads maintain their 3-dimensionality throughout the cycle. I attempted to do something similar with my own head's footage by applying CC Cylinder, but with only this effect the face becomes flat when it turns to 90 degrees.

The author of this video claimed in multiple interviews that he uses only After Effects for all of his videos, so i'm pretty sure AE was used in this one too.

Go buy a lazy suzan bearing at Home Depot, Set a chair on it. Center your head on the turning axis and put a green screen behind you. Shoot your head as you spin around.

(edit: or sit on a stool with a seat that will spin as Dave suggested)

Shoot a clean plate (the actor is not in the scene) then have the actor walk in. Roto out the head so the clean plate is in the background. Key out your spinning head green screen footage and put it between the clean plate and the rooted actor.

The guy in the video may have used AE, but don't forget -- he ALSO had a camera. And you can put a guy on a stool, spin him around, use Time Remapping to reverse the spin, and so on, and so on, and so on.....

It's very unlikely there was any 3D magic in that particular shot. Just some trick photography.